Restricted versions of the Tukey-Teichmüller theorem that are equivalent to the Boolean prime ideal theorem

Archive for Mathematical Logic 44 (4):459-472 (2005)
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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

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10.1007/s00153-004-0264-9

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Cut-conditions on sets of multiple-alternative inferences.Harold T. Hodes - 2022 - Mathematical Logic Quarterly 68 (1):95 - 106.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
The theory of Representations for Boolean Algebras.M. H. Stone - 1936 - Journal of Symbolic Logic 1 (3):118-119.
[Omnibus Review].Erwin Engeler - 1967 - Journal of Symbolic Logic 32 (2):280-281.
Eine Konstruktion von Modellerweiterungen.Erwin Engeler - 1959 - Mathematical Logic Quarterly 5 (7‐13):126-131.
Eine Konstruktion von Modellerweiterungen.Erwin Engeler - 1959 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 5 (7-13):126-131.

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