Text only print
Full screen print
Logic
Seminar information archive ～06/24｜Next seminar｜Future seminars 06/25～
| Organizer(s) | SAKAI Hiroshi, HASEGAWA Ryu |
|---|
Seminar information archive
2026/06/18
15:30-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Paul Larson (Miami University)
Discontinuous homomorphisms without Hamel bases
Paul Larson (Miami University)
Discontinuous homomorphisms without Hamel bases
[ Abstract ]
A Hamel basis for the real line is a basis for the line over the scalar field of rational numbers. The Axiom of Choice implies that Hamel bases exist. It is a classical fact that every measurable homomorphism from the additive group on the real line to itself is continuous, and therefore is given by multiplication by some real number. However, permutations of Hamel bases naturally give rise to discontinuous homomorphisms. In this talk we will show that this implication cannot be reversed, by forcing to produce a model of ZF in which there exists a discontinuous homomorphism but there is no Hamel basis. This is joint work with Saharon Shelah.
A Hamel basis for the real line is a basis for the line over the scalar field of rational numbers. The Axiom of Choice implies that Hamel bases exist. It is a classical fact that every measurable homomorphism from the additive group on the real line to itself is continuous, and therefore is given by multiplication by some real number. However, permutations of Hamel bases naturally give rise to discontinuous homomorphisms. In this talk we will show that this implication cannot be reversed, by forcing to produce a model of ZF in which there exists a discontinuous homomorphism but there is no Hamel basis. This is joint work with Saharon Shelah.
2025/11/28
13:00-14:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Ryuya Hora (The University of Tokyo)
Connectedness and full subcategories of topoi (Japanese)
Ryuya Hora (The University of Tokyo)
Connectedness and full subcategories of topoi (Japanese)
2019/12/20
13:00-14:30 Room #156 (Graduate School of Math. Sci. Bldg.)
2019/11/21
13:30-15:00 Room #156 (Graduate School of Math. Sci. Bldg.)
Kentaro Sato
Self-referential Theorems for Finitist Arithmetic
Kentaro Sato
Self-referential Theorems for Finitist Arithmetic
[ Abstract ]
The finitist logic excludes,on the syntax level, unbounded quantifiers
and accommodates only bounded quantifiers.
The following two self-referential theorems for arithmetic theories
over the finitist logic will be considered:
Tarski's impossibility of naive truth predicate and
Goedel's incompleteness theorem.
Particularly, it will be briefly explained that
(i) the naive truth theory over the finitist arithmetic with summation and multiplication
is consistent and proves its own consistency, and that
(ii) by the use of finitist arithmetic, the hierarchy of consistency strengths,
based on Goedel's second incompleteness theorem,
can be extended downward (to the area not reachable by first order predicate arithmetic).
This is a joint work with Jan Walker, and overlaps significantly with his doctoral dissertation.
The finitist logic excludes,on the syntax level, unbounded quantifiers
and accommodates only bounded quantifiers.
The following two self-referential theorems for arithmetic theories
over the finitist logic will be considered:
Tarski's impossibility of naive truth predicate and
Goedel's incompleteness theorem.
Particularly, it will be briefly explained that
(i) the naive truth theory over the finitist arithmetic with summation and multiplication
is consistent and proves its own consistency, and that
(ii) by the use of finitist arithmetic, the hierarchy of consistency strengths,
based on Goedel's second incompleteness theorem,
can be extended downward (to the area not reachable by first order predicate arithmetic).
This is a joint work with Jan Walker, and overlaps significantly with his doctoral dissertation.
2019/10/24
13:30-15:00 Room #156 (Graduate School of Math. Sci. Bldg.)
Yuya Okawa (Chiba University)
Generalizations of Bennet's results about partially conservative sentences (JAPANESE)
Yuya Okawa (Chiba University)
Generalizations of Bennet's results about partially conservative sentences (JAPANESE)
