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Forcing

  • Gaisi┬áTakeuti
  • Wilson┬áM.┬áZaring
Part of the Graduate Texts in Mathematics book series (GTM, volume 1)

Abstract

We turn now to the task of expressing
$${N_a} \vDash \ulcorner \varphi \urcorner $$
as an ­Łôť0-definable predicate
$$P\left( {{m_0}, \ldots ,{m_i};{n_0}, \ldots ,{n_j} \ulcorner \varphi \urcorner } \right)$$
where i and j depend upon ÔćÔîŁ, a = {m 0, m 1, ...} and ¤ë - a = {n 0, n 1, ...}. Such a predicate will be defined in this section. When this predicate holds we say that < {m 0, ..., m i}, {n 0, ..., n j }> forces ÔćÔîŁ. The ordered pair <{m 0, ..., m i}, {n 0, ..., n j }> is called a forcing condition.

Keywords

Induction Hypothesis Complete Sequence Force Condition Fundamental Function Axiom Schema 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

┬ę┬áSpringer-Verlag Berlin Heidelberg┬á1971

Authors and Affiliations

  • Gaisi┬áTakeuti
    • 1
  • Wilson┬áM.┬áZaring
    • 1
  1. 1.University of IllinoisUSA

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