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Nathanael Ackerman [6]Nathanael Leedom Ackerman [5]Nathanael L. Ackerman [1]
  1.  19
    Categoricity in Multiuniversal Classes.Nathanael Ackerman, Will Boney & Sebastien Vasey - 2019 - Annals of Pure and Applied Logic 170 (11):102712.
    The third author has shown that Shelah's eventual categoricity conjecture holds in universal classes: class of structures closed under isomorphisms, substructures, and unions of chains. We extend this result to the framework of multiuniversal classes. Roughly speaking, these are classes with a closure operator that is essentially algebraic closure (instead of, in the universal case, being essentially definable closure). Along the way, we prove in particular that Galois (orbital) types in multiuniversal classes are determined by their finite restrictions, generalizing a (...)
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  2.  90
    Relativized Grothendieck topoi.Nathanael Leedom Ackerman - 2010 - Annals of Pure and Applied Logic 161 (10):1299-1312.
    In this paper we define a notion of relativization for higher order logic. We then show that there is a higher order theory of Grothendieck topoi such that all Grothendieck topoi relativizes to all models of set theory with choice.
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  3.  13
    A Classification of Orbits Admitting a Unique Invariant Measure.Nathanael Ackerman, Cameron Freer, Aleksandra Kwiatkowska & Rehana Patel - 2017 - Annals of Pure and Applied Logic 168 (1):19-36.
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  4.  28
    On Transferring Model Theoretic Theorems of $${\mathcal{L}_{{\infty},\omega}}$$ L ∞, Ω in the Category of Sets to a Fixed Grothendieck Topos.Nathanael Leedom Ackerman - 2014 - Logica Universalis 8 (3-4):345-391.
    Working in a fixed Grothendieck topos Sh(C, J C ) we generalize \({\mathcal{L}_{{\infty},\omega}}\) to allow our languages and formulas to make explicit reference to Sh(C, J C ). We likewise generalize the notion of model. We then show how to encode these generalized structures by models of a related sentence of \({\mathcal{L}_{{\infty},\omega}}\) in the category of sets and functions. Using this encoding we prove analogs of several results concerning \({\mathcal{L}_{{\infty},\omega}}\) , such as the downward Löwenheim–Skolem theorem, the completeness theorem and (...)
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  5.  39
    Individual Members 2006.Martın Abadi, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Nathanael Ackerman, Bryant Adams, Klaus T. Aehlig, Fritz Aeschbach, Henry Louis Africk & Bahareh Afshari - 2006 - Bulletin of Symbolic Logic 12 (4):625-681.
  6.  36
    Individual Members 2005.Martın Abadi, Areski Nait Abdallah, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Vicente Aboites, Nathanael Ackerman, Bryant Adams, John W. Addison Jr & Sergey Adian - 2005 - Bulletin of Symbolic Logic 11 (4).
  7. Individual Members 2004.Martın Abadi, Areski Nait Abdallah, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Vicente Aboites, Nathanael Ackerman, John W. Addison Jr, Klaus T. Aehlig & Fritz Aeschbach - 2004 - Bulletin of Symbolic Logic 10 (4).
  8.  27
    Individual Members 2003.Martın Abadi, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Vicente Aboites, Nathanael Ackerman, Roger D. Acord, Zofia Adamowicz, John W. Addison Jr & Fritz Aeschbach - 2003 - Bulletin of Symbolic Logic 9 (4).
  9.  3
    Encoding Complete Metric Structures by Classical Structures.Nathanael Leedom Ackerman - 2020 - Logica Universalis 14 (4):421-459.
    We show how to encode, by classical structures, both the objects and the morphisms of the category of complete metric spaces and uniformly continuous maps. The result is a category of, what we call, cognate metric spaces and cognate maps. We show this category relativizes to all models of set theory. We extend this encoding to an encoding of complete metric structures by classical structures. This provide us with a general technique for translating results about infinitary logic on classical structures (...)
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  10.  10
    Indivisible Sets and Well‐Founded Orientations of the Rado Graph.Nathanael L. Ackerman & Will Brian - 2019 - Mathematical Logic Quarterly 65 (1):46-56.
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  11.  11
    Sheaf Recursion and a Separation Theorem.Nathanael Leedom Ackerman - 2014 - Journal of Symbolic Logic 79 (3):882-907.
    Define a second order tree to be a map between trees. We show that many properties of ordinary trees have analogs for second order trees. In particular, we show that there is a notion of “definition by recursion on a well-founded second order tree” which generalizes “definition by transfinite recursion”. We then use this new notion of definition by recursion to prove an analog of Lusin’s Separation theorem for closure spaces of global sections of a second order tree.
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  12.  17
    Vaught’s Conjecture Without Equality.Nathanael Leedom Ackerman - 2015 - Notre Dame Journal of Formal Logic 56 (4):573-582.
    Suppose that $\sigma\in{\mathcal{L}}_{\omega _{1},\omega }$ is such that all equations occurring in $\sigma$ are positive, have the same set of variables on each side of the equality symbol, and have at least one function symbol on each side of the equality symbol. We show that $\sigma$ satisfies Vaught’s conjecture. In particular, this proves Vaught’s conjecture for sentences of $ {\mathcal{L}}_{\omega _{1},\omega }$ without equality.
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