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  1. Isaac Goldbring, Bradd Hart & Thomas Sinclair (forthcoming). The Theory of Tracial von Neumann Algebras Does Not Have a Model Companion. Journal of Symbolic Logic.
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  2. Isaac Goldbring & Vinicius Cifú Lopes (2015). Pseudofinite and Pseudocompact Metric Structures. Notre Dame Journal of Formal Logic 56 (3):493-510.
    The definition of a pseudofinite structure can be translated verbatim into continuous logic, but it also gives rise to a stronger notion and to two parallel concepts of pseudocompactness. Our purpose is to investigate the relationship between these four concepts and establish or refute each of them for several basic theories in continuous logic. Pseudofiniteness and pseudocompactness turn out to be equivalent for relational languages with constant symbols, and the four notions coincide with the standard pseudofiniteness in the case of (...)
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  3. Matthias Aschenbrenner & Isaac Goldbring (2014). Transseries and Todorov–Vernaeve's Asymptotic Fields. Archive for Mathematical Logic 53 (1-2):65-87.
    We study the relationship between fields of transseries and residue fields of convex subrings of non-standard extensions of the real numbers. This was motivated by a question of Todorov and Vernaeve, answered in this paper.
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  4. Alan Dow, Isaac Goldbring, Warren Goldfarb, Joseph Miller, Toniann Pitassi, Antonio Montalbán, Grigor Sargsyan, Sergei Starchenko & Moshe Vardi (2013). Madison, WI, USA March 31–April 3, 2012. Bulletin of Symbolic Logic 19 (2).
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  5. Clifton Ealy & Isaac Goldbring (2012). Thorn-Forking in Continuous Logic. Journal of Symbolic Logic 77 (1):63-93.
    We study thorn forking and rosiness in the context of continuous logic. We prove that the Urysohn sphere is rosy (with respect to finitary imaginaries), providing the first example of an essentially continuous unstable theory with a nice notion of independence. In the process, we show that a real rosy theory which has weak elimination of finitary imaginaries is rosy with respect to finitary imaginaries, a fact which is new even for discrete first-order real rosy theories.
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  6. Isaac Goldbring (2012). An Approximate Herbrand's Theorem and Definable Functions in Metric Structures. Mathematical Logic Quarterly 58 (3):208-216.
    We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable functions in Hilbert spaces expanded by a group of generic unitary operators and Hilbert spaces expanded by a generic subspace. We also show how Herbrand's theorem can be used to characterize definable functions in absolutely ubiquitous structures from classical logic.
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  7. Isaac Goldbring (2012). Definable Operators on Hilbert Spaces. Notre Dame Journal of Formal Logic 53 (2):193-201.
    Let H be an infinite-dimensional (real or complex) Hilbert space, viewed as a metric structure in its natural signature. We characterize the definable linear operators on H as exactly the "scalar plus compact" operators.
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