Peano arithmetic and hyper-Ramsey logic

Author:
James H. Schmerl

Journal:
Trans. Amer. Math. Soc. **296** (1986), 481-505

MSC:
Primary 03H15; Secondary 03C80, 03C85, 03F35

DOI:
https://doi.org/10.1090/S0002-9947-1986-0846594-0

MathSciNet review:
846594

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Abstract: It is known that , Peano arithmetic in a language with the Ramsey quantifier, is complete and compact and that its first-order consequences are the same as those of . A logic , called hyper-Ramsey logic, is defined; it is the union of an increasing sequence of sublogics, and contains . It is proved that , which is Peano arithmetic in the context of , has the same first-order consequences as . A by-product and ingredient of the proof is, for example, the existence of a model of having the form .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0846594-0

Keywords:
Peano arithmetic,
second-order theories of arithmetic,
Ramsey quantifier,
ramified analytical hierarchy,
hyper-Ramsey logic

Article copyright:
© Copyright 1986
American Mathematical Society