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Preservation properties for iterations with finite support
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We present the classical theory of preservation of $\sqsubset$-unbounded families in generic extensions by ccc posets, where $\sqsubset$ is a definable relation of certain type on spaces of real…
A friendly iteration forcing that the four cardinal characteristics of $\mathcal{E}$ can be pairwise different
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- 2022
. Let E be the σ -ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for E , their associated cardinal…
Some Forcing Techniques : Ultrapowers , templates , and submodels
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This is an expository paper about several sophisticated forcing techniques closed related to standard finite support iterations of ccc partial orders. We focus on the four topics of ultrapowers of…
Modern Forcing Techniques related to Finite Support Iteration: Ultrapowers, templates, and submodels
- Environmental Science
- 2021
This is an expository paper about several sophisticated forcing techniques closely related to standard finite support iterations of ccc partial orders. We focus on the following four topics:…
On cardinal characteristics of Yorioka ideals
- MathematicsMath. Log. Q.
- 2019
It is shown that, consistently, the additivity and cofinality of Yorioka ideals does not coincide with the addition and co finality of the ideal of Lebesgue measure zero subsets of the real line.
Matrix Iterations with Vertical Support Restrictions
- MathematicsProceedings of the 14th and 15th Asian Logic Conferences
- 2019
We use coherent systems of FS iterations on a power set, which can be seen as matrix iteration that allows restriction on arbitrary subsets of the vertical component, to prove general theorems about…
COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS
- Physics, Computer ScienceThe Journal of Symbolic Logic
- 2018
A forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets is introduced, which are referred to as 3D-coherent systems.
Filter-linkedness and its effect on preservation of cardinal characteristics
- MathematicsAnn. Pure Appl. Log.
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MAD families and strategically bounding forcings
- MathematicsEuropean Journal of Mathematics
- 2022
Informally, a proper forcing $$\mathbb {P}$$ P is strategically bounding if there is a strategy to prove that $$\mathbb {P}$$ P is $$\omega ^{\omega }$$ ω ω -bounding. We prove that certain MAD…
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