16 found
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  1.  36
    Pseudofinite and Pseudocompact Metric Structures.Isaac Goldbring & Vinicius Cifú Lopes - 2015 - 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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  2.  13
    Thorn-Forking in Continuous Logic.Clifton Ealy & Isaac Goldbring - 2012 - 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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  3. Everettian Mechanics with Hyperfinitely Many Worlds.Jeffrey Barrett & Isaac Goldbring - forthcoming - Erkenntnis:1-20.
    The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.
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  4.  10
    Definable Closure in Randomizations.Uri Andrews, Isaac Goldbring & H. Jerome Keisler - 2015 - Annals of Pure and Applied Logic 166 (3):325-341.
  5.  20
    An Approximate Herbrand’s Theorem and Definable Functions in Metric Structures.Isaac Goldbring - 2012 - 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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  6.  23
    The Theory of Tracial von Neumann Algebras Does Not Have a Model Companion.Isaac Goldbring, Bradd Hart & Thomas Sinclair - 2013 - Journal of Symbolic Logic 78 (3):1000-1004.
  7.  4
    Dividing and Weak Quasi-Dimensions in Arbitrary Theories.Isaac Goldbring & Henry Towsner - 2015 - Archive for Mathematical Logic 54 (7-8):915-920.
    We show that any countable model of a model complete theory has an elementary extension with a “pseudofinite-like” quasi-dimension that detects dividing.
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  8.  1
    Computability and the Connes Embedding Problem.Isaac Goldbring & Bradd Hart - 2016 - Bulletin of Symbolic Logic 22 (2):238-248.
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  9.  12
    Definable Operators on Hilbert Spaces.Isaac Goldbring - 2012 - 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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  10. Continuous Sentences Preserved Under Reduced Products.Isaac Goldbring & H. Jerome Keisler - 2022 - Journal of Symbolic Logic 87 (2):649-681.
    Answering a question of Cifú Lopes, we give a syntactic characterization of those continuous sentences that are preserved under reduced products of metric structures. In fact, we settle this question in the wider context of general structures as introduced by the second author.
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  11.  7
    Continuous Sentences Preserved Under Reduced Products.Isaac Goldbring & H. Jerome Keisler - 2020 - Journal of Symbolic Logic:1-33.
    Answering a question of Cifú Lopes, we give a syntactic characterization of those continuous sentences that are preserved under reduced products of metric structures. In fact, we settle this question in the wider context of general structures as introduced by the second author.
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  12.  13
    Independence in Randomizations.Uri Andrews, Isaac Goldbring & H. Jerome Keisler - 2019 - Journal of Mathematical Logic 19 (1):1950005.
    The randomization of a complete first-order theory [Formula: see text] is the complete continuous theory [Formula: see text] with two sorts, a sort for random elements of models of [Formula: see text] and a sort for events in an underlying atomless probability space. We study independence relations and related ternary relations on the randomization of [Formula: see text]. We show that if [Formula: see text] has the exchange property and [Formula: see text], then [Formula: see text] has a strict independence (...)
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  13.  22
    Madison, WI, USA March 31–April 3, 2012.Alan Dow, Isaac Goldbring, Warren Goldfarb, Joseph Miller, Toniann Pitassi, Antonio Montalbán, Grigor Sargsyan, Sergei Starchenko & Moshe Vardi - 2013 - Bulletin of Symbolic Logic 19 (2).
  14.  3
    Scattered sentences have few separable randomizations.Uri Andrews, Isaac Goldbring, Sherwood Hachtman, H. Jerome Keisler & David Marker - 2020 - Archive for Mathematical Logic 59 (5-6):743-754.
    In the paper Randomizations of Scattered Sentences, Keisler showed that if Martin’s axiom for aleph one holds, then every scattered sentence has few separable randomizations, and asked whether the conclusion could be proved in ZFC alone. We show here that the answer is “yes”. It follows that the absolute Vaught conjecture holds if and only if every \-sentence with few separable randomizations has countably many countable models.
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  15.  5
    High Density Piecewise Syndeticity of Product Sets in Amenable Groups.Mauro di Nasso, Isaac Goldbring, Renling Jin, Steven Leth, Martino Lupini & Karl Mahlburg - 2016 - Journal of Symbolic Logic 81 (4):1555-1562.
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  16.  6
    Transseries and Todorov–Vernaeve’s Asymptotic Fields.Matthias Aschenbrenner & Isaac Goldbring - 2014 - 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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