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Surrealist landscape with figures (a survey of recent results in set theory)

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Abstract

This is the text of the hitherto unpublished article written at Stanford University and circulated in typescript in 1968 with the title page given below. “Recent” being no longer a true description of its contents, I publish it now under a timeless title by which it has been cited by other writers. In doing so, I have corrected the typographical errors in the original text but not the mathematical ones, to which attention is drawn instead in the notes on subsequent developments which will be found together with a supplementary bibliography at the end. The sign + in the text marks points on which those notes comment.

I record here my gratitude toDana Scott, then Professor of Logic at Stanford, who enabled me to spend eight stimulating months in California and whose brainchild the survey was.

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References

I. Basic references

  • [B1]R. H. Bing, A translation of the normal Moore space conjecture,Proc. Amer. Math. Soc. 16 (1965), 612–619.MR 31 # 6201

    Google Scholar 

  • [B2]E. Ellentuck, The universal properties of Dedekind finite cardinals,Ann. of Math. 82 (1965), 225–248.MR 31 # 4729

    Google Scholar 

  • [B3]W. Hanf, Incompactness in languages with infinitely long expressions,Fund. Math. 53 (1963), pp. 309–324.MR 28 # 3943

    Google Scholar 

  • [B4]H. J. Keisler andA. Tarski, From accessible to inaccessible cardinals,Fund. Math. 53 (1963), pp. 225–308.MR 29 # 3385

    Google Scholar 

  • [B5]A.Lévy, The Fraenkel—Mostowski method for independence proofs in set theory,The Theory of Models, North Holland, Amsterdam, (1965), 225–248.

    Google Scholar 

  • [B6]A Lévy,A hierarchy of formulae of set theory, Memoirs of the Amer. Math. Soc., 1966.

  • [B7]A. Lévy andR. M. Solovay, Measurable cardinals and the continuum hypothesis,Israel J. of Math. 5 (1967), 234–248.

    Google Scholar 

  • [B8]M. E. Rudin,Countable paracompactness and Souslin's problem, Canad. J. Math7 (1955), 543–547.MR 17-391

    Google Scholar 

  • [B9]W. R. Scott,Group Theory, Prentice-Hall, Englewood Cliffs, 1964,MR 29 # 4785

    Google Scholar 

  • [B10]R. M. Solovay, The measure problem I: A model of set theory in which all sets of reals are Lebesgue measurable. (In preparation)

  • [B11]R. M. Solovay, On the cardinality of∑ 12 sets of reals,Foundations of Math. (Symp.,1966,Columbus), Springer, New York, 1969, 58–73.MR 43 # 3115

    Google Scholar 

  • [B12]R. M. Solovay, A non-constructibleΔ 13 set of integers,Trans. Amer. Math. Soc. 127 (1967), 50–75.MR 35 # 2748

    Google Scholar 

  • [B13]H. Tanaka, Some properties of∑ 11 - andΠ 11 -sets inN n,Proc. Japan Acad. 42 (1966), 304–307.MR 34 # 5683

    Google Scholar 

  • [B14]R. L. Vaught, The Löwenheim—Skolem theorem,Logic, Methodology and Philos. Sci. Proc. Congr. 1964), North-Holland, Amsterdam, 1965, 81–89.MR 35 # 1461

    Google Scholar 

  • [B15]W. Reinhardt andR. M. Solovay, Strong axioms of infinity and elementary embeddings. (In preparation)

  • [B16]R. B. Jensen,Large cardinals. An English translation of lectures given at Oberwolfach in March, 1967. (To appear)

II. Supplementary references

  • [S1]C. J. Ash, A consequence of the axiom of choice,J. Austral. Math. Soc. 19 (1975), 306–308.MR 54 # 92

    Google Scholar 

  • [S2]B. Balcar, A theorem on supports in the theory of semisets,Comment. Math. Univ. Carolinae 14 (1973), 1–6.MR 49 # 4772

    Google Scholar 

  • [S3]J. E. Baumgartner, Ineffability properties of cardinals, I,Infinite and Finite Sets (Proc. Colloq. Keszthely,1973), North-Holland, Amsterdam, 1975, 109–130.MR 50 # 5427

    Google Scholar 

  • [S4]J. E. Baumgartner, A. Hajnal andA. Mété, Weak saturation properties of ideals,Infinite and Finite Sets (Proc. Colloq. Keszthely,1973) North-Holland, Amsterdam, 1975, 137–158.MR 51 # 5317

    Google Scholar 

  • [S5]J. E. Baumgartner andK. Příkry, On a theorem of Silver,Discrete Math. 14 (1976), 17–21.MR 52 # 7908

    Article  Google Scholar 

  • [S6]J. L. Bell, On the relationship between weak compactness inL ω1ω ,L ω1ω1 and restricted second-order languages,Arch. Math. Logik Grundlagenforsch. 15 (1972), 74–78.MR 48 # 1878

    Article  Google Scholar 

  • [S7]J. L. Bell andD. H. Fremlin, A geometric form of the axiom of choice,Fund. Math. 77 (1972), 167–170.MR 48 # 5865

    Google Scholar 

  • [S8]M. Benda andJ. Ketonen, Regularity of ultrafilters,Israel J. Math. 17 (1974), 231–240.MR 53 # 132

    Google Scholar 

  • [S9]M. Boffa, The consistency problem for NF.

  • [S10]W. Boos, Infinitary compactness without strong inaccessibility,J. Symbolic Logic 41 (1976), 33–38.MR 53 # 12946

    Google Scholar 

  • [S11]D. Booth, A Boolean view of sequential compactness,Fund. Math. 85 (1974), 99–102.MR 51 # 4168

    Google Scholar 

  • [S12]L. Bukovský, Characterization of generic extensions of models of set theory,Fund. Math. 83 (1973), 35–46.MR 48 # 10804

    Google Scholar 

  • [S13]G. V. Choodnovski (Čudnovskiî), Sequentially continuous mappings and real valued measurable cardinals,Infinite and Finite Sets, Proc. Colloq. Keszthely, 1973), North-Holland, Amsterdam, 1975, 275–288.

    Google Scholar 

  • [S14]G. V. Choodnovski (Čudnovskiî), Combinatorial properties of compact cardinals,Infinite and Finite Sets (Proc. Colloq. Keszthely, 1973), North-Holland, Amsterdam, 1975, 289–306.MR 51 # 7873

    Google Scholar 

  • [S15]J. H. Conway, Effective implications between the “finite” choice axioms.Cambridge Summer School in Mathematical Logic (Cambridge, England, 1971) Springer, Berlin, 1973, 439–458.MR 50 # 12725

    Google Scholar 

  • [S16]P. Dehornoy, Solution d'une conjecture de Bukovsky,C. R. Acad. Sci. Paris Sér. A-B 281 (1975), A821-A824.MR 53 # 12947

    Google Scholar 

  • [S17]K. J. Devlin,Aspects of constructibility, Springer, Berlin 1973.MR 51 # 12527

    Google Scholar 

  • [S18]K. J. Devlin, Some weak versions of large cardinal axioms.Ann. Math. Logic 5 (1973), 291–325.MR 51 # 161

    Article  Google Scholar 

  • [S19]K. J. Devlin, A note on a problem os Erdős and Hajnal,Discrete Math. 11 (1975), 9–22.MR 51 # 6842

    Article  Google Scholar 

  • [S20]K. J. Devlin andH. Johnsbråten,The Souslin problem, Springer, Berlin, 1974.MR 52 #5416

    Google Scholar 

  • [S21]T. Dodd andR. B. Jensen,The core Model.

  • [S22]F. R. Drake,Set theory an introduction to large cardinals, North-Holland Amsterdam, 1974.

    Google Scholar 

  • [S23]D. A. Edwards, Two theorems of functional analysis effectively equivalent to choice axioms,Fund. Math. 88 (1975), 95–101.MR 51 # 10094

    Google Scholar 

  • [S24]P. C. Eklof, Whitehead's problem is undecidable.

  • [S25]P. Erdős, A. Hajnal, A. Máté andR. Rado,Partition calculus.

  • [S26]U. Felgner,Models of ZF-set theory, Springer, Berlin, 1971.MR 50 # 4298

    Google Scholar 

  • [S27]U. Felgner, The independence of the Boolean prime ideal theorem from the order extension principle.

  • [S28]J. E. Fenstad, The axiom of determinateness,Proc. Second Scandinavian Logic Sympos. (Oslo, 1970), North-Holland, Amsterdam, 1971, 41–61.MR 48 # 10806

    Google Scholar 

  • [S29]W. Fleissner, Normal Moore spaces in the constructible universe,Proc. Amer. Math. Soc. 46 (1974), 294–298.MR 50 # 14682

    Google Scholar 

  • [S30]H. M. Friedman, Higher set theory and mathematical practice,Ann. Math. Logic 2 (1971), 325–357.MR 44 # 1556

    Article  Google Scholar 

  • [S31]H. Friedman, One hundred and two problems in mathematical logic,J. of Symbolic Legic 40 (1975), 113–129.MR 51 # 5254

    Google Scholar 

  • [S32]F. Galvin andA. Hajnal, Inequalities for cardinal powers,Ann. Math. 101 (1975), 491–498.MR 51 # 12535

    Google Scholar 

  • [S33]G. Gardiner, The equivalence of Boolean prime ideal theorem and a theorem of functional analysis,Fund. Math. 84 (1974), 81–86.MR 50 # 10749

    Google Scholar 

  • [S34]S. Grigorieff, Combinatorics on ideals and forcing,Ann. Math. Logic 3 (1971), 363–394.MR 45 # 6614

    Article  Google Scholar 

  • [S35]S. Grigorieff, Intermediate submodels and generic extensions in set theory,Ann. Math. 101 (1975), 447–490.MR 51 # 10089

    Google Scholar 

  • [S36]D. Guaspari,Thin and wellordered analytical sets, University of Cambridge, 1973. (Ph. D. Thesis)

  • [S37]D. Guaspari, The largest countableΠ 11 .

  • [S38]L. Harrington,Π 21 sets andΠ 21 singletons,Proc. Amer. Math. Soc. 52 (1975), 356–360.MR 51 # 10096

    Google Scholar 

  • [S39]L. Harrington, Long projective wellorderings.

  • [S40]L. Harrington, The constructable reals can be (almost) anything.

  • [S41]L. Harrington andT. Jech, OnΣ 1 well orderings of the universe,J. Symbolic Logic 41 (1976), 167–170.MR 53 # 7780

    Google Scholar 

  • [S42]J. Harrison, Recursive pseudo-well-orderings,Trans. Amer. Math. Soc. 131 (1968), 526–543.MR 39 # 5366

    Google Scholar 

  • [S43]P. E. Howard, Limitations on the Fraenkel-Mostowski method of independence proofs,J. Symbolic Logic 38 (1973), 416–422.MR 52 # 2878

    Google Scholar 

  • [S44]P. E. Howard, Los's theorem plus the Boolean prime ideal theorem imply the axiom of choice,Proc. Amer. Math. Soc. 49 (1975), 426–428.MR 52 # 5422

    Google Scholar 

  • [S45]T. J. Jech,Lectures in set theory with particular emphasis on the method of forcing, Springer, Berlin, 1971.MR 48 # 105

    Google Scholar 

  • [S46]T. J. Jech, Forcing with trees and ordinal definability,Ann. Math. Logic 7 (1975), 387–409.MR 51 # 142

    Article  Google Scholar 

  • [S47]T. J. Jech,The axiom of choice, North-Holland, Amsterdam, 1973.MR 53 # 139

    Google Scholar 

  • [S48]T. J. Jech, Trees,J. Symbolic Logic 36 (1971), 1–14.MR 44 # 1560

    Google Scholar 

  • [S49]T. J. Jech, Some combinatorial problemsn concernig uncountable cardinals,Ann. Math. Logic 5 (1973), 165–198.Zbl.262. 02062

    Article  Google Scholar 

  • [S50]T. Jech andK. Příkry, On ideals of sets and the power set operation.

  • [S51]R. Jensen, Definable sets of minimal degree, in:Mathematical Logic and Foundations of Set Theory (ed. Y. Bar-Hillel), North-Holland, Amsterdam, 1970.

    Google Scholar 

  • [S52]R. B. Jensen, Coding the universe by a real.

  • [S53]R. B. Jensen, Marginalia to a theorem of Silver (with two subsequent corrections: More Marginalia; Marginalia III). See the paper byDevlin andJensen,Proc. Logic Colloq. (Kiel, 1974), Springer, Berlin, 1975.

  • [S54]R. B. Jensen, The fine structure of the constructible hierarchy,Ann. Math. Logic 4 (1972), 229–308 and 443.MR 46 # 8834

    Article  Google Scholar 

  • [S55]R. B. Jensen, On the consistency of a slight (?) modification of Quine's New Foundations,Synthese 19 (1968), 250–263.Zbl.202. 10

    Article  Google Scholar 

  • [S56]R. B. Jensen andH. Johnsbråten, A new construction of a non-constructibleΔ 13 subset of ω,Fund. Math. 81 (1974), 279–290.MR 52 # 13382

    Google Scholar 

  • [S57]R. R. Jensen andB. Koppelberg, A note on ultrafilters (and an Addendum)

  • [S58]R. B. Jensen andK. Kunen,Some combinatorial properties of L and V. (Manuscript)

  • [S59]R. B. Jensen andR. M. Solovay, Some applications of almost disjoint sets,Mathematical Logic and Foundations of Set Theory (Proc. Colloq., Jerusalem, 1968), North-Holland, Amsterdam, 1970, 84–104.MR 44 # 6482

    Google Scholar 

  • [S60]A. Kanamori,Ultrafilters over uncountable cardinals, University of Cambridge, 1975. (Ph. D. Thesis)

  • [S61]A. Kanamori, Wenkly normal filters and irregular ultrafilters.

  • [S62]A. Kanamori, W. N. Reinhardt andR. Solovay, Strong axioms of infinity and elementary embeddings,Ann. Math. Logic. (To appear)

  • [S63]A. S. Kechris, The theory of countable analytical sets,Trans. Amer. Math. Soc. 202 (1975), 259–297.MR 54 # 7259

    Google Scholar 

  • [S64]A. S. Kechris, Measure and category in effective descriptive set theory,Ann. Math. Logic 5 (1973), 337–384.MR 51 # 5308

    Article  Google Scholar 

  • [S65]A. S. Kechris, On projective ordinals,J. Symbolic Logic 39 (1974), 269–282MR 54 # 2684

    Google Scholar 

  • [S66]A. S. Kechris andY. N. Moschovakis,Notes on the theory of scales. (Typescript)

  • [S67]J. Ketonen, Strong compactness and other cardinal sins.Ann. Math. Logic 5 (1972), 47–76.Zbl 257. 02055

    Article  Google Scholar 

  • [S68]J. Ketonen, Non-regular ultrafilters and large cardinals,Trans. Amer. Math. Soc. 224 (1976), 61–73.MR 54 # 7260

    Google Scholar 

  • [S69]E. M. Kleinberg, Rowbottom cardinals and Jónsson cardinals are almost the same,J. Symbolic Logic 38 (1973), 423–427.MR 43 # 2385

    Google Scholar 

  • [S70]E. M. Kleinberg, AD The ℵ Π are Jónsson cardinals and ℵ ω is a Rowbottom cardinal.

  • [S71]K. Kunen, Some applications of iterated ultrapowers in set theory,Ann. Math. Logic 1 (1970), 179–227.MR 43 # 3080

    Article  Google Scholar 

  • [S72]K. Kunen, On the GCH at Measurable Cardinals,Proc. Colloq (Manchester 1969), North-Holland, Amsterdam, 1971, 107–110.MR 43 # 3081

    Google Scholar 

  • [S73]K. Kunen, A model for the negation of the axiom of choice,Cambridge Summer School in Mathematical Logic (Cambridge, England, 1971), Springer, Berlin, 1973, 489–494.MR 49 # 2372

    Google Scholar 

  • [S74]K. Kunen, Saturated ideals.

  • [S75]K. Kunen andJ. B. Paris, Boolean extension and measurable cardinals,Ann. Math. Logic 2 (1971), 359–377.MR 43 # 3114

    Article  Google Scholar 

  • [S76]J. Lake, Natural models and Ackermann-type set theories,J. Symbolic Logic 40 (1975), 151–158.MR 51 # 5307

    Google Scholar 

  • [S77]R. Laver, on the consistency of Borel's conjecture.

  • [S78]A. Lévy andR. M. Solovay, On the decomposition of sets of reals to Borel sets,Ann. Math. Logic 5 (1972), 1–20.MR 47 # 38

    Article  Google Scholar 

  • [S79]M. Magidor, On the singular cardinals problem, I–II.

  • [S80]M. Magidor, How large is the first strongly compact cardinal? or Study in Identity Crises,Ann. Math. Logic 10 (1976), 33–59

    Article  Google Scholar 

  • [S81]R. Mansfield, The non-existence ofΣ 12 well-orderings of the Cantor set,Fund. Math. 86 (1976), 279–282.MR 52 # 7903

    Google Scholar 

  • [S82]R. Mansfield, Omitting types: application to descriptive set theory,Proc. Amer. Math. Soc. 47 (1975), 198–200.MR 50 # 6851

    Google Scholar 

  • [S83]W. Marek andM. Srebrny, Gaps in the constructible universe,Ann. Math. Logic 6 (1974), 359–394.MR 51 # 10102

    Article  Google Scholar 

  • [S84]D. A. Martin, Measurable cardinals and analytic games,Fund. Math. 66 (1960), 281–291.MR 41 # 3283

    Google Scholar 

  • [S85]D. A. Martin, Borel determinacy,Ann. of Math. 102 (1975), 363–371.MR 53 # 7785

    Google Scholar 

  • [S86]D. A. Martin, Projective sets and cardinal numbers.

  • [S87]D. A. Martin andJ. B. Paris, AD implies that there are exactly two normal measures onω 2

  • [S88]D. A. Martin, andR. M. Solovay, Internal Cohen extension,Ann. Math. Logic 2 (1970), 143–178.MR 42 # 5787

    Article  Google Scholar 

  • [S89]A. R. D. Mathias, Happy Families,Ann. Math. Logic (To appear)

  • [S90]A. R. D. Mathias, On sequences generic in the sense of Příkry,J. Austral. Math. Soc. 15 (1973), 409–414.MR 48 # 10809

    Google Scholar 

  • [S91]K. McAloon, On the sequence of models HODt,Fund. Math. 82 (1974), 85–93.MR 50 # 98

    Google Scholar 

  • [S92]K. McAloon, Consistency results about ordinal definability,Ann. Math. Logic 2 (1971), 449–467.MR 45 # 1753

    Article  Google Scholar 

  • [S93]T. K. Menas, On strong compactness and super-compactness,Ann. Math. Logic 7 (1975) 327–359.MR 50 # 9589

    Article  Google Scholar 

  • [S94]T. K. Menas,On strong compactness and supercompactness, University of California, Berkeley, 1974. (Ph. D. Thesis)

    Google Scholar 

  • [S95]W. J. Mitchell, Sets constructible from sequences of ultrafilters,J. Symbolic Logic 39 (1974), 57–66.MR 49 # 8863

    Google Scholar 

  • [S96]W. Mitchell, Aronszajn trees and the independence of the transfer property,Ann. Math. Logic 5 (1972), 21–46.MR 47 # 1612

    Article  Google Scholar 

  • [S97]G. P. Monro, Decomposable cardinals,Fund. Math. 80 (1973), 101–104.MR 48 # 3741

    Google Scholar 

  • [S98]C. Morgenstern, On the independence of the ordering of certain large cardinals.

  • [S99]D. B. Morris,Adding total indiscernibles to models of set theory, University of Wisconsin, Madison, 1970. (Thesis)

    Google Scholar 

  • [S100]Y. N. Moschovakis, Determinancy and prewellorderings of the continuum,Mathematical Logic and Foundations of Set Theory (Proc. Colloq., Jerusalem, 1968), North-Holland, Amsterdam, 1970, 24–62.MR 43 # 6082

    Google Scholar 

  • [S101]A. J. Ostaszewski, On countably compact, perfectly normal spaces,J. London Math. Soc. 14 (1976), 505–516.

    Google Scholar 

  • [S102]D. Pincus, Support structures for the axiom of choice,J. Symbolic Logic 36 (1971), 28–38.MR 44 # 61

    Google Scholar 

  • [S103]D. Pincus, Zermelo—Fraenkel consistency results by Fraenkel—Mostowski methods,J. Symbolic Logic 37 (1972), 721–743.MR 49 # 2374

    Google Scholar 

  • [S104]D. Pincus, The strength of the Hahn—Banach theorem,Victoria Sympos. Nonstand. Analysis (1972), Springer, Berlin, 1974, 203–248.Zbl 279. 02044

    Google Scholar 

  • [S105]K. Příkry, Changing measurable into accessible cardinals,Dissertationes Math. Rozprawy Mat. 68 (1970).MR 41 # 6685

  • [S106]K. Příkry, On a problem of Gillamn and Keisler,Ann. Math. Logic 2 (1970), 179–187.MR 42 # 4408

    Article  Google Scholar 

  • [S107]K. Příkry, Determinateness and partitions,Proc. Amer. Math. Soc. 54 (1976), 303–306.

    Google Scholar 

  • [S108]W. N. Reinhardt, Ackermann's set theory equals ZF,Ann. Math. Logic 2 (1970), 189–249.MR 43 # 42

    Article  Google Scholar 

  • [S109]F. Rothberger, Eine Äquivalenz zwischen der Kontinuumhypothese und der Existenz der Lusinschen und Sierpińskischen Mengen,Fund. Math. 30 (1938), 215–217.Zbl 18, 394

    Google Scholar 

  • [S110]F. Rowbottom, Some strong axioms of infinity incompatible with the axiom of constructibility,Ann. Math. Logic. 3 (1971), 1–44.MR 48 # 1928

    Article  Google Scholar 

  • [S111]M. E. Rudin,Lectures on set theoretic topology, American Mathematical Society, Regional Conference Series in Mathematics, No. 23.

  • [S112]G. Sageev, An independence result concerning the axiom of choice,Ann. Math. Logic 8 (1975), 1–184.MR 51 # 2915

    Article  Google Scholar 

  • [S113]S. Shelah, Infinite abelian groups Whitehead problem and some constructions,Israel J. Math. 18 (1974), 243–256.MR 50 # 9582

    Google Scholar 

  • [S114]S. Shelah, A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals,Israel J. Math. 21 (1975), 319–349.MR 52 # 10410

    Google Scholar 

  • [S115]R. A. Shore, Square bracker partition relations inL, Fund. Math. 84 (1974), 101–106.MR 51 # 7880

    Google Scholar 

  • [S116]J. H. Silver, On the singular cardinals problem,Proc. International Congress of Mathematicians, Vancouver 1974, 265–268.

  • [S117]J. H. Silver, Some applications of model theory in set theory,Ann. Math. Logic 3 (1971), 45–110.MR 53 # 12950

    Article  Google Scholar 

  • [S118]J. H. Silver, Measurable cardinals andΔ 13 well-orderings,Ann. Math. 94 (1971), 414–446MR 45 # 8517

    Google Scholar 

  • [S119]R. M. Solovay, Hyperarithmetically encodable sets.

  • [S120]R. M. Solovay, A model of set-theory in which every set of reals is Lebesgue measurable,Ann. Math. 92 (1970) 1–56.MR 42 # 64

    Google Scholar 

  • [S121]R. M. Solovay, Strongly compact cardinals and the GCH,Proc. Tarski Symposium (Berkeley, California, 1971), Amer. Math. Soc., Providence, R. I., 1974, 365–372.MR 52 # 106

    Google Scholar 

  • [S122]R. M. Solovay andS. Tennenbaum, Iterated Cohen extension and Souslin's problem,Ann. Math. 94 (1971), 201–245.MR 45 # 3212

    Google Scholar 

  • [S123]F. D. Tall, The countable chain condition versus separability—applications of Martin's axiom,General Topology and Appl. 4 (1974), 315–339.MR 54 # 11264

    Article  Google Scholar 

  • [S124]F. Tall, An alternative to the continuum hypothesis and its uses in general topology.

  • [S125]A. Tarski, Ideale in vollständigen Mengenkörpern, II.Fund. Math. 33 (1945), 51–56.MR 8 # 193

    Google Scholar 

  • [S126]J. Truss, On successors in cardinal arithmetic,Fund. Math. 78 (1973), 7–21.MR 47 # 8307

    Google Scholar 

  • [S127]J. Truss, Finite axioms of choice,Ann. Math. Logic 6 (1973), 147–176.Zbl 273. 02049

    Article  Google Scholar 

  • [S128]J. Truss, Models of set theory containing many perfect sets,Ann. Math, Logic 7 (1974), 197–219.MR 51 # 5304

    Google Scholar 

  • [S129]S. Ulam, Zur Maßtheorie in der allgemeinen Mengenlehre,Fund. Math. 16 (1930), 140–150.

    Google Scholar 

  • [S130]P. Vopěnka andP. Hájek,The theory of semisets, North-Holland, Amsterdam, 1972

    Google Scholar 

  • [S131]S. Wagon,Decompositions of saturated ideals, Darthmouth College, Hanover, New Hampshire, 1975. (Ph. D. Thesis)

    Google Scholar 

  • [S132]N. H. Williams,Cardinal numbers with partition properties, Australian National University, Canberra, 1969. (Ph. D. Thesis)

    Google Scholar 

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  1. Peterhouse college, CB2 1RD, Cambridge, England

    A. R. D. Mathias

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Work on the original version was supported by NSF Grant 7655.

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Mathias, A.R.D. Surrealist landscape with figures (a survey of recent results in set theory). Period Math Hung 10, 109–175 (1979). https://doi.org/10.1007/BF02025889

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