Properties of Cohesive Powers

Rumen Dimitrov

Knots in Washington XLIV
April 28-30, 2017
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Properties of Cohesive Powers
by
Rumen Dimitrov
Department of Mathematics, Western Illinois University, Macomb IL 61455
Coauthors: Some of the work is based on a manuscript with co-authors R. Dimitrov, P. Shafer, A. Soskova, and S. Vatev.

Cohesive powers of computable fields were used (in [1]) to characterize the principal filters of quasimaximal spaces with extendable bases in the lattice L^*(V_∞) . In [2] we used the isomorphism properties of cohesive powers of Q to classify the orbits of the equivalence classes of such spaces in the lattice L^*(V_∞). In this talk I will prove different model theoretic properties of the cohesive powers of various computable structures.

[1] R.D. Dimitrov, A class of Σ₃⁰ modular lattices embeddable as principal filters in L^*(V_∞), Archive for Mathematical Logic 47 (2008), pp. 111-132.

[2] R.D. Dimitrov and V. Harizanov, Orbits of maximal vector spaces, Algebra and Logic 54 (2015), pp. 680-732 (Russian); (2016) pp. 440-477 (English translation).

[3] R.D. Dimitrov, P. Shafer, A. Soskova, and S. Vatev, Notes on cohesive powers and Fraïssé limits, in preparation.

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Date received: April 2, 2017