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1. Nonstandard Analysis


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      Problem 1.1.

      [Jerome Keisler] Study the “reverse mathematics" of nonstandard analysis.


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          Problem 1.2.

          [Ward Henson] Is there a combinatorial result which implies $\Pi^1_1$ comprehension and has a proof in nonstandard analysis?


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              Problem 1.3.

              [Terence Tao] Give a nonstandard analysis proof of Szemerédi’s Theorem in the spirit of the original proof.


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                  Problem 1.4.

                  [Isaac Goldbring] Study boundary amenable groups from the perspective of nonstandard analysis.

                  1. Give an “internal" algebraic description of boundary amenability.

                  2. Prove analogs of the results of Di Nasso, Goldbring, Jin, Leth, Lupini, and Mahlburg, such as on high piecewise syndeticity ([MR3580478], [MR3341782]), which has been generalized to the free group.


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                      Problem 1.5.

                      [Isaac Goldbring] Give a nonstandard analysis description of Bohr sets in $\Z$.

                          Cite this as: AimPL: Nonstandard methods in combinatorial number theory, available at http://aimpl.org/nscombinatorial.