2016 9 27 RIMS
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1983 9-1989 6 University of Illinois at Chicago (UIC) John T Baldwin
1983 9-1989 6 University of Illinois at Chicago (UIC) John T Baldwin Y N Moschovakis, Descriptive Set Theory North Holland, 1980
1983 9-1989 6 University of Illinois at Chicago (UIC) John T Baldwin Y N Moschovakis, Descriptive Set Theory North Holland, 1980 UIC TA
1980 UIC UIC Logic Course Herbert B Enderton, A Mathematical Introduction to Logic, Academic Press, 1972
1980 UIC UIC Logic Course Herbert B Enderton, A Mathematical Introduction to Logic, Academic Press, 1972 Baldwin John T Baldwin, Fundamentals of Stability Theory, Springer, 1988
1980 UIC UIC Logic Course Herbert B Enderton, A Mathematical Introduction to Logic, Academic Press, 1972 Baldwin John T Baldwin, Fundamentals of Stability Theory, Springer, 1988 Pillay Anand Pillay, An introduction to stability theory, Clarendon P, Oxford, 1983
Mid-West Model Theory University of Illinois at Chicago John T Baldwin, David Marker University of Illinois Urbana-Champaign Lou van den Dries University of Notre Dame Anand Pillay, Sergei Starchenko (Byunghan Kim)
M M φ T T T
M M φ T T T 1 Th(M) 2 T
L A, B L- L- φ A = φ B = φ A B A B
L A, B L- L- φ A = φ B = φ A B A B A B A B L
1 T L- A, B T A B = A B
1 T L- A, B T A B = A B =
T L- T A, B T
T L- T A, B T T
T I(T, κ) T 1 κ T κ I(T, κ)
T I(T, κ) T 1 κ T κ I(T, κ) I(T, κ) = 1 κ- I(T, κ) = 1 T κ
2 (Morley, 1965) κ I(T, κ) = 1 κ I(T, κ) = 1 M Morley, Categoricity in power, TAMS, 1965
2 (Morley, 1965) κ I(T, κ) = 1 κ I(T, κ) = 1 M Morley, Categoricity in power, TAMS, 1965 ACF 0 0 ACF p p
T
L ω1 ω 3 (Scott ) L A L- L ω1 ω φ L- B B = φ B A
L ω1 ω 3 (Scott ) L A L- L ω1 ω φ L- B B = φ B A L ω ω L ω ω
Vaught Martin Martin
Vaught 4 Ṭ I(T, ℵ 0 ) > ℵ 0 I(T, ℵ 0 ) = 2 ℵ 0 S Shelah, L Harrington and M Makkai, A proof of Vaught s conjecture for totally transcendental theories, Israel J M 1984
Vaught 4 Ṭ I(T, ℵ 0 ) > ℵ 0 I(T, ℵ 0 ) = 2 ℵ 0 S Shelah, L Harrington and M Makkai, A proof of Vaught s conjecture for totally transcendental theories, Israel J M 1984 Vaught T
Martin 1 T S(T ) L ω ω { φ p φ : p S(T )} L ω1 ω L 1 (T )
Martin 1 T S(T ) L ω ω { φ p φ : p S(T )} L ω1 ω L 1 (T ) 5 I(T, ℵ 0 ) < 2 ℵ 0 T M Th L1 (T )(M) T T L 1 (T )
Martin 2 E Bouscalen, Martin s Conjecture for ω-stable theories, Israel J M 1984 C W Wagner, On Martin s Conjecture, Annals of Math Logic, 1982
Martin Vaught 6 Ṃartin = Vaught
Martin 1 7 ( Martin ) T S(T ) ℵ 0 (1) I(T, ℵ 0 ) < 2 ℵ 0 T M Th L1 (T )(M) (2) T L 1 2 ℵ 0
Martin 1 7 ( Martin ) T S(T ) ℵ 0 (1) I(T, ℵ 0 ) < 2 ℵ 0 T M Th L1 (T )(M) (2) T L 1 2 ℵ 0 T T L 1 (T ) T T L 1 -
Martin 2 SMC Wagner, 1982 PhD Thesis Baldwin ω-
Martin 2 SMC Wagner, 1982 PhD Thesis Baldwin ω- M I, On the strong Martin Conjecture, J S L, 1991 ω- Martin
Martin 2 SMC Wagner, 1982 PhD Thesis Baldwin ω- M I, On the strong Martin Conjecture, J S L, 1991 ω- Martin Shelah Vaught L 1 (T )
Martin 2 SMC Wagner, 1982 PhD Thesis Baldwin ω- M I, On the strong Martin Conjecture, J S L, 1991 ω- Martin Shelah Vaught L 1 (T ) ω- L 1 (T )-
S Shelah, Classification Theory and the Number of Nonisomorphic Models, North-Holland, 1978
S Shelah, Classification Theory and the Number of Nonisomorphic Models, North-Holland, 1978 S Shelah, Classification Theory for Abstract Elementary Classes, Studies in Logic vol 18 and 20, Col Pub 2009 J T Baldwin, Categoricity Univ Lect Series, vol 50, Amer Math Soc, 2009
1980 Hrushovski
(R, +,, 0, 1, <) RCF
(R, +,, 0, 1, <) RCF (C, +,, 0, 1) ACF p p 0
L M L- M M
L M L- M M (C, +,, 0, 1) Zilber Zilber Hrushovski 1980
Hrushovski, Zilber 1991
Hrushovski, Zilber 1991 Zariski P
Hrushovski, Zilber 1991 Zariski P M P M
Hrushovski, Zilber 1991 Zariski P M P M Zilber
Hrushovski, Zilber 1991 Zariski P M P M Zilber E Hrushovski and B Zilber, Zariski Goemetries, J of AMS, 1996
(M, <, ) M < M M
(M, <, ) M < M M (R, +,, 0, 1, <) 8 (Pillay, Steinhorn, Knight) Ṃ M N N
Wilkie 9 Ṛ exp 1991 1996 A J Wilkie, Model completeness results for expansions of the ordered fields of real numbers by restricted Pfaffian functions and the exponential function, J of the AMS, 1996
Pila-Wilkie R (R, +,, 0, 1, <) 10 (Pila-Wilkie, 2006) X R n R ε > 0 t 0 = t 0 (ε) t t 0 X trans (Q, t) t ε J Pila and A J Wilkie, The rational points of a definable set, Duke Math J, 133, No 3, 2006, 591-616
R exp
R exp R an
R exp R an R an,exp
R exp R an R an,exp
Mordell-Lang Hrushovski 11 ( Mordell-Lang ) k 0 KA X A K Γ A(K ) Stab X (1) (2) (1) X Γ X (2) A B k 0 S S k 0 X 0 B S k0 K h X = a 0 + h 1 ( X 0 k0 K ) E Hrushovski, The Mordell-Lang conjecture for function fields, Jour AMS, 1996
Hrushovski X Γ X k 0 k 0 X 0 X 0 h
Hrushovski X Γ X k 0 k 0 X 0 X 0 h 0 Buium
Hrushovski X Γ X k 0 k 0 X 0 X 0 h 0 Buium Hrushovski Buium 0
Hrushovski X Γ X k 0 k 0 X 0 X 0 h 0 Buium Hrushovski Buium 0
Pila (2011) J Pila O-minimality and the André-Oort conjecture for C n Ann of Math 173(2011), 1779-1840
Pila (2011) J Pila O-minimality and the André-Oort conjecture for C n Ann of Math 173(2011), 1779-1840 V C n X V = X X
Pila (2011) J Pila O-minimality and the André-Oort conjecture for C n Ann of Math 173(2011), 1779-1840 V C n X V = X X André-Oort
Pila Pila-Wilkie X
Pila Pila-Wilkie X (Siegel ) X
Pila Pila-Wilkie X (Siegel ) X X < X
B Zilber, Zariski Geometries, Geometry from Logician s Point of View, London Math Soc Lect Note Series, 360, 2010
B Zilber, Zariski Geometries, Geometry from Logician s Point of View, London Math Soc Lect Note Series, 360, 2010
M I, and Boris Zilber, Notes on a model theory of a quantum 2-torus T 2 q for generic q, arxive:150306045v1, 2015 2- L ω1 ω- L ω ω - 12 2-
Logics
Logics
Logics L ω ω
Logics L ω ω