3,245 research outputs found
Pure patterns of order 2
We provide mutual elementary recursive order isomorphisms between classical
ordinal notations, based on Skolem hulling, and notations from pure elementary
patterns of resemblance of order , showing that the latter characterize the
proof-theoretic ordinal of the fragment - of second
order number theory, or equivalently the set theory . As a
corollary, we prove that Carlson's result on the well-quasi orderedness of
respecting forests of order implies transfinite induction up to the ordinal
of . We expect that our approach will facilitate analysis of
more powerful systems of patterns.Comment: corrected Theorem 4.2 with according changes in section 3 (mainly
Definition 3.3), results unchanged. The manuscript was edited, aligned with
reference [14] (moving former Lemma 3.5 there), and argumentation was
revised, with minor corrections in (the proof of) Theorem 4.2; results
unchanged. Updated revised preprint; to appear in the APAL (2017
Game semantics for first-order logic
We refine HO/N game semantics with an additional notion of pointer
(mu-pointers) and extend it to first-order classical logic with completeness
results. We use a Church style extension of Parigot's lambda-mu-calculus to
represent proofs of first-order classical logic. We present some relations with
Krivine's classical realizability and applications to type isomorphisms
Energy functions on moduli spaces of flat surfaces with erasing forest
Flat surfaces with erasing forest are obtained by deforming the flat metric structure of translation surfaces, the moduli space of such surfaces is a deformation of the moduli space of translation surfaces. On the moduli space of flat surfaces with erasing forest, one can define some energy function involving the area of the surface, and the total length of the erasing forest. Note that on this space, we have a volume form which is defined by using geodesic triangulations. The aim of this paper is to prove that the integral of the energy functions mentionned above with respect to this volume form is finite. As applications, we will use this result to recover some classical results due to Masur-Veech, and Thurston
Triangulations and volume form on moduli spaces of flat surfaces
In this paper, we are interested in flat metric structures with conical
singularities on surfaces which are obtained by deforming translation surface
structures. The moduli space of such flat metric structures can be viewed as
some deformation of the moduli space of translation surfaces. Using geodesic
triangulations, we define a volume form on this moduli space, and show that, in
the well-known cases, this volume form agrees with usual ones, up to a
multiplicative constant.Comment: 42 page
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