Iterated elementary embeddings and the model theory of infinitary logic

DOI10.1016/j.apal.2015.12.004zbMath1432.03056OpenAlexW2184669491MaRDI QIDQ904149

John T. Baldwin, Paul B. Larson

Publication date: 12 January 2016

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2015.12.004

zbMATH Keywords

absolutenessabstract elementary classesGalois typesiterated elementary embeddings

Mathematics Subject Classification ID

Descriptive set theory (03E15) Classification theory, stability, and related concepts in model theory (03C45) Other infinitary logic (03C75) Set-theoretic model theory (03C55) Generic absoluteness and forcing axioms (03E57) Abstract elementary classes and related topics (03C48)

Related Items

An example related to Gregory's theorem, Abstract elementary classes stable in \(\aleph_{0}\), Iterated ultrapowers for the masses, A strong failure of \(\aleph _0\)-stability for atomic classes, Structural logic and abstract elementary classes with intersections

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Categoricity, amalgamation, and tameness
• Abstract elementary classes and infinitary logics
• Martin's maximum, saturated ideals, and nonregular ultrafilters. I
• Categoricity in \(\aleph_1\) of sentences in \(L_{\omega_1\omega}(Q)\)
• A weak version of \(\lozenge\) which follows from \(2^{\aleph_0}<2^{\aleph_1}\)
• The Hanf number of stationary logic
• Non-forking frames in abstract elementary classes
• Independence in finitary abstract elementary classes
• Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers
• Forcing over Models of Determinacy
• The amalgamation spectrum
• ALMOST GALOIS ω-STABLE CLASSES
• On Certain Elementary Extensions of Models of Set Theory
• A reflection phenomenon in descriptive set theory
• Generalized Quantifiers and Compact Logic
• Elementary extensions of countable models of set theory
• Stationary logic
• A uniqueness theorem for iterations
• Model Theory
• AMALGAMATION, ABSOLUTENESS, AND CATEGORICITY
• An interpolation theorem for denumerably long formulas
• Elementary extensions of models of set theory