Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn some applications of strongly compact Prikry forcing
81
0
0.0
(
0
)
Authors
Amitayu Banerjee
Ask ChatGPT about the research
No Arabic abstract
We work with symmetric inner models of forcing extensions based on strongly compact Prikry forcing to extend some known results.
rate research
Read More
Given an inner model $W subset V$ and a regular cardinal $kappa$, we consider two alternatives for adding a subset to $kappa$ by forcing: the Cohen poset $Add(kappa,1)$, and the Cohen poset of the inner model $Add(kappa,1)^W$. The forcing from $W$ will be at least as strong as the forcing from $V$ (in the sense that forcing with the former adds a generic for the latter) if and only if the two posets have the same cardinality. On the other hand, a sufficient condition is established for the poset from $V$ to fail to be as strong as that from $W$. The results are generalized to $Add(kappa,lambda)$, and to iterations of Cohen forcing where the poset at each stage comes from an arbitrary intermediate inner model.
We revisit Kolchins results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological fields, which encompasses ordered or p-valued differential fields, we find a partial Galois correspondence and we show one cannot expect more in general. In the class of ordered differential fields, using elimination of imaginaries in CODF, we establish a relative Galois correspondence for relatively definable subgroups of the group of differential order automorphisms.
We give a detailed proof of Kolchins results on differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. We closely follow former works due to Pillay and his co-authors which were written under the assumption that the field of constant is algebraically closed. In the present setting, which encompasses the cases of ordered or p-valued differential fields, we find a partial Galois correspondence and we show one cannot expect more in general. In the class of ordered differential fields, using elimination of imaginaries in the theory of closed ordered fields, we establish a relative Galois correspondence for definable subgroups of the group of differential order automorphisms.
In this paper, motivated by a question posed in cite{AH}, we introduce strongly biconvex graphs as a subclass of weakly chordal and bipartite graphs. We give a linear time algorithm to find an induced matching for such graphs and we prove that this algorithm indeed gives a maximum induced matching. Applying this algorithm, we provide a strongly biconvex graph whose (monomial) edge ideal does not admit a unique extremal Betti number. Using this constructed graph, we provide an infinite family of the so-called closed graphs (also known as proper interval graphs) whose binomial edge ideals do not have a unique extremal Betti number. This, in particular, answers the aforementioned question in cite{AH}.
We study the class of Borel equivalence relations under continuous reducibility. In particular , we characterize when a Borel equivalence relation with countable equivalence classes is $Sigma$ 0 $xi$ (or $Pi$ 0 $xi$). We characterize when all the equivalence classes of such a relation are $Sigma$ 0 $xi$ (or $Pi$ 0 $xi$). We prove analogous results for the Borel equivalence relations with countably many equivalence classes. We also completely solve these two problems for the first two ranks. In order to do this, we prove some extensions of the Louveau-Saint Raymond theorem which itself generalized the Hurewicz theorem characterizing when a Borel subset of a Polish space is G $delta$ .
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
