论文信息 - Hilbert versus Hindman

Hilbert versus Hindman

We show that a statement HIL, which is motivated by a lemma of Hilbert and close in formulation to Hindman’s theorem, is actually much weaker than Hindman’s theorem. In particular, HIL is finitistically reducible in the sense of Hilbert’s program, while Hindman’s theorem is not.

Jeffry L. Hirst

[1] Wilfried Sieg,et al. Fragments of arithmetic , 1985, Ann. Pure Appl. Log..

[2] Stephen G. Simpson,et al. Partial realizations of Hilbert's program , 1988, Journal of Symbolic Logic.

[3] Paul Erdös,et al. Quantitative Forms of a Theorem of Hilbert , 1985, J. Comb. Theory, Ser. A.

[4] Jeff B. Paris,et al. A Hierarchy of Cuts in Models of Arithmetic , 1980 .

[5] Stephen G. Simpson,et al. Subsystems of second order arithmetic , 1999, Perspectives in mathematical logic.

[6] Stephen G. Simpson,et al. Logical analysis of some theorems of combinatorics and topological dynamics , 1987 .

[7] D. Hilbert. Ueber die Irreducibilität ganzer rationaler Functionen mit ganzzahligen Coefficienten. , 1892 .