Canonical truth

Philipp Schlicht; Merlin Carl

doi:10.1007/s10516-022-09631-5

Canonical truth

Philipp Schlicht , Merlin Carl

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

We introduce and study some variants of a notion of canonical set theoretical truth. By this, we mean truth in a transitive proper class model M of ZFC that is uniquely characterized by some ∈-formula. We show that there are interesting statements that hold in all such models, but do not follow from ZFC, such as the ground model axiom and the nonexistence of measurable cardinals. We also study a related concept in which we only require M to be fixed up to elementary equivalence. We show that this theory-canonicity also goes beyond provability in ZFC, but it does not rule out measurable cardinals and it does not fix the size of the continuum.

Original language	English
Pages (from-to)	785-803
Journal	Axiomathes
Volume	32
Early online date	Aug 2022
DOIs	https://doi.org/10.1007/s10516-022-09631-5
Publication status	E-pub ahead of print - Aug 2022

Access to Document

10.1007/s10516-022-09631-5Licence: CC BY

Handle.net

Persistent link

Cite this

@article{d204780f20854e32bdaf2ad4198a6723,

title = "Canonical truth",

abstract = "We introduce and study some variants of a notion of canonical set theoretical truth. By this, we mean truth in a transitive proper class model M of ZFC that is uniquely characterized by some ∈-formula. We show that there are interesting statements that hold in all such models, but do not follow from ZFC, such as the ground model axiom and the nonexistence of measurable cardinals. We also study a related concept in which we only require M to be fixed up to elementary equivalence. We show that this theory-canonicity also goes beyond provability in ZFC, but it does not rule out measurable cardinals and it does not fix the size of the continuum.",

author = "Philipp Schlicht and Merlin Carl",

year = "2022",

month = aug,

doi = "10.1007/s10516-022-09631-5",

language = "English",

volume = "32",

pages = "785--803",

journal = "Axiomathes",

}

TY - JOUR

T1 - Canonical truth

AU - Schlicht , Philipp

AU - Carl, Merlin

PY - 2022/8

Y1 - 2022/8

N2 - We introduce and study some variants of a notion of canonical set theoretical truth. By this, we mean truth in a transitive proper class model M of ZFC that is uniquely characterized by some ∈-formula. We show that there are interesting statements that hold in all such models, but do not follow from ZFC, such as the ground model axiom and the nonexistence of measurable cardinals. We also study a related concept in which we only require M to be fixed up to elementary equivalence. We show that this theory-canonicity also goes beyond provability in ZFC, but it does not rule out measurable cardinals and it does not fix the size of the continuum.

AB - We introduce and study some variants of a notion of canonical set theoretical truth. By this, we mean truth in a transitive proper class model M of ZFC that is uniquely characterized by some ∈-formula. We show that there are interesting statements that hold in all such models, but do not follow from ZFC, such as the ground model axiom and the nonexistence of measurable cardinals. We also study a related concept in which we only require M to be fixed up to elementary equivalence. We show that this theory-canonicity also goes beyond provability in ZFC, but it does not rule out measurable cardinals and it does not fix the size of the continuum.

U2 - 10.1007/s10516-022-09631-5

DO - 10.1007/s10516-022-09631-5

M3 - Article (Academic Journal)

VL - 32

SP - 785

EP - 803

JO - Axiomathes

JF - Axiomathes

ER -

Canonical truth

Abstract

Access to Document

Handle.net

Fingerprint

Cite this