TWO-SORTED FREGE ARITHMETIC IS NOT CONSERVATIVE

DOI10.1017/s1755020322000156zbMath1530.00011OpenAlexW4224071056MaRDI QIDQ6148472

Jeremy Avigad, Stephen Mackereth

Publication date: 11 January 2024

Published in: The Review of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1755020322000156

zbMATH Keywords

FregeHume's principlelogicismsecond-order logicconservative extensionsecond-order arithmeticneologicismneo-Fregeanismabstractionismfield-conservativenessstipulative definition

Mathematics Subject Classification ID

Philosophy of mathematics (00A30) Philosophical and critical aspects of logic and foundations (03A05) Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35)

Cites Work

• Neo-Fregeanism: an embarrassment of riches
• Some criteria for acceptable abstraction
• Double vision: two questions about the neo-Fregean program
• Proof theory. 2nd ed
• Cardinality and acceptable abstraction
• Conservativeness, Stability, and Abstraction
• Abstraction Reconceived
• Developing arithmetic in set theory without infinity: some historical remarks
• Speaking with Shadows: A Study of Neo‐Logicism
• New V, ZF and Abstraction†
• DEDUCTIVE CARDINALITY RESULTS AND NUISANCE-LIKE PRINCIPLES
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