Work

Inner models from extended logics: Part 2

Year: 2025

Type: article

Abstract: We introduce a new inner model [Formula: see text] arising from stationary logic. We show that assuming a proper class of Woodin cardinals, or alternatively PFA, the regular uncountable cardinals of [Formula: see text] are measurable in the inner model [Formula: see text] and [Formula: see text] satisfies CH. Moreover, assuming a proper class of Woodin cardinals, the theory of [Formula: see text] is (set) forcing absolute. We introduce an auxiliary concept that we call Club Determinacy, which simplifies the construction of [Formula: see text] greatly but may have also independent interest. Based on Club Determinacy, we introduce the concept of aa-mouse which we use to prove CH and other properties of the inner model [Formula: see text].

Source: Journal of Mathematical Logic

DOI: 10.1142/s0219061325500096

Authors: Juliette Kennedy, Menachem Magidor, Jouko Väänänen

Institutions: University of Helsinki, Hebrew University of Jerusalem, University of Amsterdam

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Helsingin Yliopisto, European Commission, Academy of Finland

Awards: G4652034890, G658088708