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Logic
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Organizer(s) | Toshiyasu Arai |
|---|
Seminar information archive
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)
