Add to ORKGMatatyahu Rubin has shown that a sharp version of Vaught's conjecture, $I({\mathcal T},\omega )\in \{ 0,1,{\mathfrak{c}}\}$, holds for each complete theory of linear order ${\mathcal T}$. We show that the same is true for each complete theory of partial order having a model in the the minimal class of partial orders containing the class of linear orders and which is closed under finite products and finite disjoint unions. The same holds for the extension of the class of rooted trees admitting a finite monomorphic decomposition, obtained in the same way. The sharp version of Vaught's conjecture also holds for the theories of trees which are infinite disjoint unions of linear orders.Comment: 27 page
We investigate minimal rst-order structures and consider interpretability and denability of ordering...
A partial order is called semilinear if the upper bounds of each element are linearly ordered and an...
Is the Vaught Conjecture model theory? Possible simple answer: Yes, because it is true at certain le...
Let $T$ be a countable complete first-order theory with a definable, infinite, discrete linear order...
We introduce the $\omega$-Vaught's conjecture, a strengthening of the infinitary Vaught's conjecture...
Introduced by Kodama and Williams, Bruhat interval polytopes are generalized permutohedra closely co...
Vaught’s Conjecture states that if T is a complete first order theory in a countable language such t...
Trees are partial orderings where every element has a linearly ordered set of smaller elements. We d...
AbstractWe say that a linear ordering L is extendible if every partial ordering that does not embed ...
The Vaught Conjecture is a notorious open problem in mathematical logic. A number of stronger conjec...
We show that Morley's theorem on the number of countable models of a countable first-order theory be...
The Ordered conjecture of Kolaitis and Vardi asks whether fixed-point logic differs from first-order...
Vaught's Conjecture states that if T is a complete First order theory in a countable language that ...
A long-standing conjecture of Sacks states that it is provable in ZFC that every locally countable p...
We consider the classes of finite coloured partial orders, i.e., partial orders together with unary ...
We investigate minimal rst-order structures and consider interpretability and denability of ordering...
A partial order is called semilinear if the upper bounds of each element are linearly ordered and an...
Is the Vaught Conjecture model theory? Possible simple answer: Yes, because it is true at certain le...
Let $T$ be a countable complete first-order theory with a definable, infinite, discrete linear order...
We introduce the $\omega$-Vaught's conjecture, a strengthening of the infinitary Vaught's conjecture...
Introduced by Kodama and Williams, Bruhat interval polytopes are generalized permutohedra closely co...
Vaught’s Conjecture states that if T is a complete first order theory in a countable language such t...
Trees are partial orderings where every element has a linearly ordered set of smaller elements. We d...
AbstractWe say that a linear ordering L is extendible if every partial ordering that does not embed ...
The Vaught Conjecture is a notorious open problem in mathematical logic. A number of stronger conjec...
We show that Morley's theorem on the number of countable models of a countable first-order theory be...
The Ordered conjecture of Kolaitis and Vardi asks whether fixed-point logic differs from first-order...
Vaught's Conjecture states that if T is a complete First order theory in a countable language that ...
A long-standing conjecture of Sacks states that it is provable in ZFC that every locally countable p...
We consider the classes of finite coloured partial orders, i.e., partial orders together with unary ...
We investigate minimal rst-order structures and consider interpretability and denability of ordering...
A partial order is called semilinear if the upper bounds of each element are linearly ordered and an...
Is the Vaught Conjecture model theory? Possible simple answer: Yes, because it is true at certain le...