Potential isomorphism and semi-proper trees

• Autorzy: Alex Hellsten , Tapani Hyttinen , Saharon Shelah
• Języki publikacji: EN

Abstrakty

EN

We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the cardinality of the models. We introduce the notion of weakly semi-proper trees, and note that there is a strong connection between the existence of potentially isomorphic models for a given complete theory and the existence of weakly semi-proper trees.
We show that the existence of weakly semi-proper trees is consistent relative to ZFC by proving the existence of weakly semi-proper trees under certain cardinal arithmetic assumptions. We also prove the consistency of the non-existence of weakly semi-proper trees assuming the consistency of some large cardinals.

Kategorie tematyczne

• 03E05: Other combinatorial set theory
• 03C55: Set-theoretic model theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 175
• Numer: 2
• Strony: 127-142

Daty

wydano

2002

Twórcy

autor

Alex Hellsten

• Department of Mathematics, University of Helsinki, 00014 Helsinki, Finland

autor

Tapani Hyttinen

• Department of Mathematics, University of Helsinki, 00014 Helsinki, Finland

autor

Saharon Shelah

• Institute of Mathematics, The Hebrew University, 91904 Jerusalem, Israel
• Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, U.S.A.

Identyfikatory

DOI

10.4064/fm175-2-3