Set Theorem – The relationship between Martin's axiom, the countable chain condition, and the Knaster property

This is a repetition of a question that remained unanswered in MSE

We say that a poset $ P $ has the Knaster property (or is Knaster) when every innumerable subset of $ P $ contains an uncountable subset of pairwise compatible conditions.

To let $ K $ denote the statement "every c.c.c. poset is knaster" and leave $ P $ denote the statement "the product of $ 2 $ c.c.c. posets is c.c.c. ". Then we have $ mathsf {MA} _ { aleph_1} implies K implies P $,

From the comments on the MSE question, I learned that Todorčević's work "Forcing with a Cohesive Souslin Tree" states that it is an open problem whether the first implication is reversible. Has there been any progress since this paper was written or is it still open? What is known about whether the second implication is an iff?

uri – NOTE: Attempting to use property & # 39; nid & # 39; to retrieve a non-object

In Drupal rsvplist Form RSVPForm-> buildForm () I wrote the following to get the current NID:

$node = Drupal::routeMatch()->getParameter('node');
$nid = $node->nid->value;

I get this error:

Note: An attempt is made to use the property & # 39; nid & # 39; of a non-object in retrieve
Drupal rsvplist Form RSVPForm-> buildForm () (line 30 of
modules custom rsvplist src Form RSVPForm.php).

I am a new module developer. How do I get the current NID in Drupal 8?

Active Directory – Can the administrator assign the device property in O365 AD to another user?

As an O365 Global Admin, I added a new device to the O365 Active Directory (Cloud only). I have added the new user on the device and they have logged in and are working. However, in the O365 admin panel, the device appears as owner with my administrator ID. Is it possible to reassign the device owner as a user?

Native React – × TypeError: Undefined location property can not be read

Good night, I'm trying to find api.js, but I have to go back to the directory, but ReactNative gives bugs, can not find the way, already tried

Import API from & # 39; ../../ services / api & # 39 ;;
and
Import API from & # 39; ../ ../services/api&#39 ;;

but he still can not find the way, could someone help me?

API design – error codes with property files or databases

Error code! = Enum

Your error code is not an enumeration, but a separate object.

Enumeration (and constants in general) are great ways to code the initialization value of an error code.

They are awful like the storage unit itself. For as you emphasize, a receiver that defines the error code as an enumeration determines what "legal" error codes are, even though it has the least amount of information about it.

Identity, category and semantics

So, what do you mean when you say? error code?

  • Is it a unique identifier that describes a specific error condition?
  • Is it a categorical identifier that describes a class of errors?
  • Is it an instruction that describes how the recipient of the error should respond?
  • Or a combination of the above?

The only place that knows the error code is the place where it is generated. (Hopefully confirmed by reasonable unit tests.)

Everywhere else, whether in the same application or in the distance, the exact value does not matter. What you are interested in are functions (serialization) and questions (network problems, can I try again?).

distribution

The other problem you have encountered is that you are sharing the same responsibility among multiple actors.

This is no different than other types of messages that are transmitted between systems. I recommend defining the protocol of each interface. Any system that operates through this interface must be mapped and retrieved from this protocol in any meaningful way.

This is painful, but it is separate software. By increasing the coupling between them by forcing a common idea of ​​error code (apart from what is defined in the interface protocol between them) both parts of the software become more brittle.

Cheeky – not just because they need to use the same version of the library – but because they need to synchronize the appropriate uses of unique identifying error codes and generally agree fully with the categories and semantics of error codes.

You could improve the brittleness by insisting on backward compatibility, but that's a snake's own cage.

fa.functional analysis – An extreme property of points on the unit sphere of a two-dimensional Banach space

To let $ (X, | cdot |) $ to be a two-dimensional real Banach space and $ S = {x in X: | x | = 1 } $ be his unit sphere. Accept that $ S $ is smooth in the sense that for everyone $ y in S $ There is a unique feature $ y ^ *: X to mathbb R $ so that $ y ^ * (y) = 1 = | y ^ * | $, This unique feature $ y ^ * $ that will mean supportive functional at the $ y $,

To let $ x, y in S $ Be points, so that $$ | y-x | + | y + x | = max { | s-x | + | s + x |: s in S }. $$

Question. is $ y ^ * (x) = 0 $?

In an object list, look for the property that matches 2 criteria

I am trying to inherit the property (which is a Boolean value) of an object in which it is stored in a list <>, which I add as follows:

 Logger.lstEnvio.Add(new OperationResultTO() { Id = Guid.NewGuid(), Job = "Dashboard", IsSend = false });

I have to find both IsSend = false and IsSend = true in the list.

initially only those in IsSend = false were queried like this:

 var results = Logger.lstEnvio.FindAll(b => b.IsSend== false);

As I explained above, I also need to get those that are true in the same variable results

Induction – Detecting the k-inductance of a property with an SMT solver (parametrically resettable counter)

I follow the slides at https://homepage.cs.uiowa.edu/~tinelli/talks/FT-11.pdf, where Tinelli explains how k-induction works in the context of SMT-based model validation.

A parametric and resettable counter is specified as a Kripke structure by the following formulas:

Variables:

  • $ x: = (c, n, r, n_0) $, Where:
    • $ n_0 $ is a positive integer
    • $ r $ is an input Boolean value
    • $ c $. $ n $ are internal integer variables

Initialization:

  • $ I (x): = (c = 1) Wedge (n = n_0) $

Transitions:

  • $ begin {align *}
    T (x, x)): = (n; = n) & Wedge (((V = (c = n)) & to (c = = 1) ) \
    & wedge (& neg (r & # 39; vee (c = n)) & to (c & # 39; = c + 1)) \
    end {align *} $

Property that proves invariable:

Tinelli uses the following notation:

$ I ^ i: = I (x ^ {(i)}), P ^ i: = P (x ^ {(i)}), T ^ i: = T (x ^ {(i-1)}, x ^ {(i)}) $,

He then claims on page 52/90 that the formula $ P: = c le n + 1 $ is an invariant of this system because $ P $ is 1-inductive (while by the way is not 0-inductive). If I follow correctly, that means that $ I ^ 0 models P ^ 0 $ and $ I ^ 0 Wedge T ^ 1 Models P ^ 1 $ (Base case) and $ P ^ 0 wedge P ^ 1 wedge T ^ 1 wedge T ^ 2 models P ^ 2 $ (inductive stage). In particular, it means that the formula $ P ^ 0 Wedge P ^ 1 Wedge T ^ 1 Wedge T ^ 2 Wedge Neg (P ^ 2) $ is OURS. After playing a bit with Z3Py, I was able to find the following model for this formula and a corresponding representation of a state transition $ (c, n, r) $:

  • $ c ^ 0 = -1, n ^ 0 = 0, c ^ 1 = 1, n ^ 1 = 0, r ^ 1 = text {True}, c ^ 2 = 2, n ^ 2 = 0, r ^ 2 = text {False} $
  • $ (- 1, 0, *) to (1, 0, text {True}) to (2, 0, text {False}) $

Intuitively, that makes sense. The restriction on $ n_0 $ A positive integer affects the base case formula $ I ^ 0 $ but not the inductive stage, and therefore the above model is a valid model of the induction formula for $ i = 1 $ which means that the implication fails.

Of course $ P $ is an invariant of this system, but it seems to me that we can not show it with k induction for k = 1.

What is the gap in my understanding of this material?