Abstract
The notion of formal space was introduced by Fourman and Grayson [FG] only a few years ago, but it is only a recent though important step of a long story whose roots involve such names as Brouwer and Stone and whose development is due to mathematicians from different fields, mainly algebraic geometry, category theory and logic.
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References
M. Fourman — R. Grayson, Formal spaces, in: The L.E.J. Brouwer Centenary Symposium, eds. A. S. Troelstra and D. van Dalen, North Holland 1982, pp. 107–122
J. W. Gray, Fragments of the history of sheaf theory, in: Applications of Sheaves, eds. M. Fourman, C. Mulvey and D. Scott, Springer 1979, pp. 1–79
P. Johnstone, Stone spaces, Cambridge U. P. 1982
S. C. Kleene — R. E. Vesley, The foundations of intuitionistic mathematics, North Holland 1965
P. Martin-Löf, Intuitionistic type theory, Bibliopolis, Napoli 1984
P. Martin-Löf, On the meanings of logical constants and the justifications of logical laws, in: Atti degli Incontri di Logica Matematica v. 2, eds. C. Bernardi and P. Pagli, Dip. di Matem., Univ. di Siena, Siena 1985, pp. 203–281
P. Martin-Löf, Unifying Scott’s theory of domains for denotational semantics and intuitionistic type theory, in: Logica e Filosofia della Scienza, oggi. San Gimi-gnano, 7–11 Dicembre 1983, v.1, CLUEB, Bologna 1986, pp. 79–83
E. Martino — P. Giaretta, Brouwer, Dummett and the bar theorem, in: Atti del Convegno Nazionale di Logica, Montecatini Terme, 1–5 ottobre 1979, Bibliopolis, Napoli 1981, pp. 541–558
D. Scott, Lectures on a mathematical theory of computation, Oxford Univ. Computing Lab.,Techn. Monograph PRG-19, 1981
D. Scott, Domains for denotational semantics, in: Automata, Languages and Programming, eds. M. Nielsen and E. M. Schmidt, Springer 1982, pp. 577–613
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© 1987 Plenum Press, New York
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Sambin, G. (1987). Intuitionistic Formal Spaces — A First Communication. In: Skordev, D.G. (eds) Mathematical Logic and Its Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0897-3_12
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DOI: https://doi.org/10.1007/978-1-4613-0897-3_12
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