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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 11U: Connections with logic

Introduction

History

Applications and related fields

Subfields

• 11U05: Decidability [See also 03B25]
• 11U07: Ultraproducts [See also 03C20]
• 11U09: Model theory [See also 03Cxx]
• 11U10: Nonstandard arithmetic [See also 03H15]
• 11U99: None of the above, but in this section

Parent field: 11: Number Theory

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

A nice survey is by Beukers, F. and Manin, Yu. I.: "Diophantine equations", Nieuw Arch. Wisk. (4) 7 (1989) 3--13.

Software and tables

Other web sites with this focus

• Hilbert's Tenth Problem page [Maxim Vsemirnov under supervision of Yuri Matijasevic}

Selected topics at this site

• Statements in number theory whose truth is independent of the Peano axioms (e.g. the Paris-Harrington statement).
• Find values for the 26-variable integer polynomial yielding primes
• Conway's generalizations of the Collatz conjecture include some undecidable problems