On Logical Sentences in PA

Saharon Shelah

doi:10.1016/S0049-237X(08)71815-9

On Logical Sentences in PA

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The chapter discusses the Paris–Harrington partition theorem (PH), which is used to prove the consistency of Peano arithmetic (PA). A finitary π⁰₂ combinatorial principle capturing π¹₁-CA_O, based on end-homogeneity instead of homogeneity is presented._. The method of producing theories with incomparable and equal consistency strength along is demonstrated along with examples.

Original language	English
Pages (from-to)	145-160
Number of pages	16
Journal	Studies in Logic and the Foundations of Mathematics
Volume	112
Issue number	C
DOIs	https://doi.org/10.1016/S0049-237X(08)71815-9
State	Published - 1 Jan 1984

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10.1016/S0049-237X(08)71815-9

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title = "On Logical Sentences in PA",

abstract = "The chapter discusses the Paris–Harrington partition theorem (PH), which is used to prove the consistency of Peano arithmetic (PA). A finitary π02 combinatorial principle capturing π11-CAO, based on end-homogeneity instead of homogeneity is presented.. The method of producing theories with incomparable and equal consistency strength along is demonstrated along with examples.",

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AB - The chapter discusses the Paris–Harrington partition theorem (PH), which is used to prove the consistency of Peano arithmetic (PA). A finitary π02 combinatorial principle capturing π11-CAO, based on end-homogeneity instead of homogeneity is presented.. The method of producing theories with incomparable and equal consistency strength along is demonstrated along with examples.

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JO - Studies in Logic and the Foundations of Mathematics

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IS - C

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On Logical Sentences in PA

Abstract

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