A proofless proof of the Barwise compactness theorem

Journal of Symbolic Logic 53 (2):597-602 (1988)
  Copy   BIBTEX

Abstract

We prove a theorem (1.7) about partial orders which can be viewed as a version of the Barwise compactness theorem which does not mention logic. The Barwise compactness theorem is easily equivalent to 1.7 + "Every Henkin set has a model". We then make the observation that 1.7 gives us the definability of forcing for quantifier-free sentences in the forcing language and use this to give a direct proof of the truth and definability lemmas of forcing

Categories

Keywords

Reprint years

DOI

10.2307/2274526

Other Versions

No versions found

Links

PhilArchive

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Karp Carol. An algebraic proof of the Barwise compactness theorem. The syntax and semantics of infinitary languages, edited by Barwise Jon, Lecture notes in mathematics, no. 72, Springer-Verlag, Berlin, Heidelberg, and New York, 1968, pp. 80–95.Carol Karp & Jon Barwise - 1974 - Journal of Symbolic Logic 39 (2):335-335.
Steel forcing and barwise compactness.Sy D. Friedman - 1982 - Annals of Mathematical Logic 22 (1):31-46.
An algebraic treatment of the Barwise compactness theory.Isidore Fleischer & Philip Scott - 1991 - Studia Logica 50 (2):217 - 223.
Generalizations of Kochen and Specker's theorem and the effectiveness of Gleason's theorem.Ehud Hrushovski & Itamar Pitowsky - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (2):177-194.
Random variables and integral logic.Karim Khanaki & Seyed-Mohammad Bagheri - 2011 - Mathematical Logic Quarterly 57 (5):494-503.
Three Model-Theoretic Constructions for Generalized Epstein Semantics.Krzysztof A. Krawczyk - 2022 - Review of Symbolic Logic 15 (4):1023-1032.
Definability and automorphisms in abstract logics.Xavier Caicedo - 2004 - Archive for Mathematical Logic 43 (8):937-945.
On Transferring Model Theoretic Theorems of $${\mathcal{L}_{{\infty},\omega}}$$ L ∞, ω in the Category of Sets to a Fixed Grothendieck Topos.Nathanael Leedom Ackerman - 2014 - Logica Universalis 8 (3-4):345-391.
Supercompactness and level by level equivalence are compatible with indestructibility for strong compactness.Arthur W. Apter - 2007 - Archive for Mathematical Logic 46 (3-4):155-163.
A forcing notion related to Hindman’s theorem.Luz María García-Ávila - 2015 - Archive for Mathematical Logic 54 (1-2):133-159.

Analytics

Added to PP
2009-01-28

Downloads
157 (#267,110)

6 months
28 (#329,238)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Add more citations

References found in this work

No references found.

Add more references