Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Itay Kaplan"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 12 (2024)
We initiate a systematic study of generic stability independence and introduce the class of treeless theories in which this notion of independence is particularly well behaved. We show that the class of treeless theories contains both binary theories
Externí odkaz:
https://doaj.org/article/be195298dab149598b12fe77ce03a071
Publikováno v:
The Journal of Symbolic Logic. 87:1349-1373
The notion of a complete type can be generalized in a natural manner to allow assigning a value in an arbitrary Boolean algebra B to each formula. We show some basic results regarding the effect of the properties of B on the behavior of such types, a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0685a696bba5fb37cfc15831fc325819
https://doi.org/10.1017/jsl.2022.7
https://doi.org/10.1017/jsl.2022.7
Publikováno v:
The Journal of Symbolic Logic. 86:1508-1540
We show that the countable universal homogeneous meet-tree has a generic automorphism, but it does not have a generic pair of automorphisms.
Comment: 33 pages (incl. references); very minor corrections, references and MSC update
Comment: 33 pages (incl. references); very minor corrections, references and MSC update
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ec68cbf18ad15edf18a7435a51b42227
https://doi.org/10.1017/jsl.2021.9
https://doi.org/10.1017/jsl.2021.9
Autor:
Nicholas Ramsey, Itay Kaplan
Publikováno v:
Journal of the European Mathematical Society. 22:1423-1474
We study NSOP$_{1}$ theories. We define Kim-independence, which generalizes non-forking independence in simple theories and corresponds to non-forking at a generic scale. We show that Kim-independence satisfies a version of Kim's lemma, local charact
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d8ead3ceddd2b817c9f14b01d57f91f2
https://doi.org/10.4171/jems/948
https://doi.org/10.4171/jems/948
Autor:
Itay Kaplan, Yatir Halevi
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 168:601-612
A generalisation of von Staudt’s theorem that every permutation of the projective line that preserves harmonic quadruples is a projective semilinear map is given. It is then concluded that any proper supergroup of permutations of the projective sem
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::83b1b10c9ac3983889f65e1268706a72
https://doi.org/10.1017/s0305004119000021
https://doi.org/10.1017/s0305004119000021
Autor:
Shlomo Eshel, Itay Kaplan
Publikováno v:
Journal of Mathematical Logic. 21
Combining two results from machine learning theory we prove that a formula is NIP if and only if it satisfies uniform definability of types over finite sets (UDTFS). This settles a conjecture of Laskowski.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::675190c2e3c5f61fdabec75f3dbc56bd
https://doi.org/10.1142/s021906132150015x
https://doi.org/10.1142/s021906132150015x
We use exact saturation to study the complexity of unstable theories, showing that a variant of this notion called pseudo-elementary class (PC)-exact saturation meaningfully reflects combinatorial dividing lines. We study PC-exact saturation for stab
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b6e289a653688cbc1a3ef534dc6b2b9
http://arxiv.org/abs/2009.08365
http://arxiv.org/abs/2009.08365
Publikováno v:
Proceedings of the American Mathematical Society. 147:1719-1732
We show that NSOP$_{1}$ theories are exactly the theories in which Kim-independence satisfies a form of local character. In particular, we show that if $T$ is NSOP$_{1}$, $M\models T$, and $p$ is a type over $M$, then the collection of elementary sub
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::297d3d3535ca0718757c14ef060b3576
https://doi.org/10.1090/proc/14305
https://doi.org/10.1090/proc/14305
Publikováno v:
Annals of Pure and Applied Logic. 172:102992
We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give criteria for a th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::32cccb6abf208196527985895a09c2a0
https://doi.org/10.1016/j.apal.2021.102992
https://doi.org/10.1016/j.apal.2021.102992
Autor:
Itay Kaplan, Pedro Andrés Estevan
Publikováno v:
Annals of Pure and Applied Logic. 172:102946
We investigate the question of whether the restriction of an NIP type p ∈ S ( B ) which does not fork over A ⊆ B to A is also NIP, and the analogous question for dp-rank. We show that if B contains a Morley sequence I generated by p over A, then
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c8cb6f757767d1b6972734dac443717f
https://doi.org/10.1016/j.apal.2021.102946
https://doi.org/10.1016/j.apal.2021.102946