Date:
Wed, 21/01/202611:00-13:00
Zoom link: https://huji.zoom.us/j/87919026478?pwd=NOaUlXLOEyRcTlFHLHoJQWgwSsXH0E.1
Meeting ID: 879 1902 6478
Passcode: 060233
Title: n-variable theorems of NCTP, NBTP, and NSOP3
Abstract: In this talk, we show that if a theory T has CTP (BTP), then there exists a witness of CTP (BTP, respectively), such that the length of the free variable part is equal to the algebraic dimension of the types given by the consistent patterns. These observations can be viewed as weakened versions of one-variable theorems that hold at many known dividing lines. We show that the n-variable theorems can play the roles that one-variable theorems do in geometric theories. Namely, if a theory T is geometric, then it is NCTP (NBTP) if and only if its generic trivialization is NCTP (NBTP), if and only if its lovely pair expansion is NCTP (NBTP), and if and only if its H-structure expansion is NCTP (NBTP, respectively). In the SOP3 case, we show similar results to the above, assuming acl=dcl additionally.
Meeting ID: 879 1902 6478
Passcode: 060233
Title: n-variable theorems of NCTP, NBTP, and NSOP3
Abstract: In this talk, we show that if a theory T has CTP (BTP), then there exists a witness of CTP (BTP, respectively), such that the length of the free variable part is equal to the algebraic dimension of the types given by the consistent patterns. These observations can be viewed as weakened versions of one-variable theorems that hold at many known dividing lines. We show that the n-variable theorems can play the roles that one-variable theorems do in geometric theories. Namely, if a theory T is geometric, then it is NCTP (NBTP) if and only if its generic trivialization is NCTP (NBTP), if and only if its lovely pair expansion is NCTP (NBTP), and if and only if its H-structure expansion is NCTP (NBTP, respectively). In the SOP3 case, we show similar results to the above, assuming acl=dcl additionally.