Restricted versions of the Tukey-Teichmüller theorem that are equivalent to the Boolean prime ideal theorem |
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Authors: | RE Hodel |
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Institution: | (1) Mathematics Department, Duke University, Durham, NC 27708, USA |
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Abstract: | We formulate a restricted version of the Tukey-Teichmüller Theorem that we denote by (rTT). We then prove that (rTT) and (BPI) are equivalent in ZF and that (rTT) applies rather naturally to several equivalent forms of (BPI): Alexander Subbase Theorem, Stone Representation Theorem, Model Existence and Compactness Theorems for propositional and first-order logic. We also give two variations of (rTT) that we denote by (rTT)+ and (rTT)++; each is equivalent to (rTT) in ZF. The variation (rTT)++ applies rather naturally to various Selection Lemmas due to Cowen, Engeler, and Rado.Dedicated to W.W. Comfort on the occasion of his seventieth birthday. |
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