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The
seminar is held in hybrid
format, in person (Múzeum
krt. 4/i Room 224) and
online at the following
link:
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| 20
February (Friday)
4:15 PM Room 224 +
ONLINE |
János
Balázs Ivanyos
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Institute of Mathematics,
Eötvös Loránd University,
Budapest
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| Algebraic
characterisation of
pseudo-elementary and
second-order classes
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In this talk I
will present purely algebraic
(model-theoretic)
characterisations for classes
definable in second-order logic
and for pseudo-elementary classes
(including PC and PC∆
classes). Classical results of
this flavour include
Keisler–Shelah type theorems
(characterising first-order
definability by closure under
ultraproducts and ultraroots) and
Birkhoff’s HSP theorem.
Here we resolve several open
problems from [2] and [1].
Our main results are the
following.
• We solve the
long-standing problem of giving a
purely algebraic character-
isation of pseudo-elementary
classes: we characterise PC∆
and PC classes by intrinsic
closure properties.
• We provide a
structural classification of
second-order equivalent structures
(that is, we give a second-order
version of the Keisler–Shelah
isomorphism theorem) and obtain
purely algebraic characterisations
of the classes definable by
second-order formulas as well as
those definable by finitely many
second-order sentences.
Technically, our approach blends
ultraproduct and Henkin semantics
with the analysis of the topology
of appropriate formula-spaces
(certain subspaces of 2κ).
With these tools we aim to provide
a new perspective on the
understanding of axiomatisability
phenomena.
References
[1] G. Sági,
Ultraproducts and Higher Order
Formulas, Math. Logic Quar- terly,
Vol. 48, No. 2, pp. 261–275,
(2002).
[2] Keisler, H.
Jerome. Limit ultraproducts. The
Journal of Symbolic Logic
30.2 (1965): 212-234.
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| 27
February (Friday)
4:15 PM Room 224 +
ONLINE |
Armand
Mazloumian
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Department
of Logic, Institute of
Philosophy,
Eötvös Loránd University,
Budapest
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| Formalizing
Hegel in paraconsistent
Logic |
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My master's dissertation
examines the contemporary trend
of formalizing not only Hegel’s
Logic but the Hegelian
dialectical process itself. To
that end, I try to develop two
technical apparatus: first, a
combination of modal and
paraconsistent logics; and
second, a combination of dynamic
and paraconsistent logics, with
the aim of providing a framework
for the formalization of Hegel’s
dialectical progression of
categories. The aim is not to
mathematize Hegel for its own
sake, but to elucidate the
elusive structure of his thought
using formal tools.
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